38 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I'm confused. Are you really going to try to make this sort of distinction when teaching geometric figures to students "around 9-13 years old"? Students that age (and engineers my age -- ...
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  • 525
24 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

One encounters exactly the same issue teaching multivariable calculus when one treats integrals over three-dimensional regions and integrals over the surfaces that are their boundaries. In particular ...
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  • 5,083
21 votes
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Metonymy in mathematics

Metonymy and its relatives, metaphor, polysemy, synecdoche occur all over the place in mathematical writing, and sometimes cause students problems and sometimes don't, because those thought processes ...
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21 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I think the distinction you are raising is not natural to students at this age. I teach undergraduates and graduate students, not elementary schoolers, but I find that it is not natural for ...
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19 votes

Can we save the word "unique"?

I don't see this as a major issue, nor do I believe that the word "unique" is in any particular need of saving. There are a large number of terms in mathematics which correspond to ...
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17 votes

Uninsulting way to say "this will eventually be easy"

Perhaps not pointing out that the obvious steps are obvious but that the insights are insights. I believe students don't feel bad for not seeing the "magic steps" by themselves, so pointing out that ...
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16 votes

Can students tell the difference between the "definition if" and the "theorem if"?

Not formal research, but some decades of experience teaching both undergrad and graduate level courses, and "editing" PhD theses and such: It appears that even many serious professional ...
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  • 13.5k
13 votes

Examples of Mathematical Slang

One of the most colorful names I have heard is the Chicken Mc Nugget theorem: for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ ...
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13 votes

What is it called when terms disappear when reducing fractions?

So German "$b$ kürzt sich weg" becomes in English "$b$ cancels out". We may also say "$b$ is eliminated".
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  • 6,211
12 votes
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Uninsulting way to say "this will eventually be easy"

One thing that you might want to do early on in your course is think about the classroom norms that you wish to establish. From your post, it seems like an example of a norm in your class is that it ...
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11 votes

Examples of Mathematical Slang

In Central Mexico, the expression \begin{equation} x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{equation} that solves quadratic equations of the form $ax^2 + bx + c = 0$ is called "fórmula del ...
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11 votes

What's the common word for equations and inequalities?

My phrase has always been math "statement". Equations and inequalities clearly assert/state a relationship between two or more things. My go-to direction using this would be something like: &...
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  • 7,686
11 votes

How to reduce ambiguity in the following question?

The ambiguous answer is relatively correct (actually you need to know how old they are at the start of the problem). But each fission is an individual splitting, not a generation. Perhaps this: A ...
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  • 111
10 votes

Uninsulting way to say "this will eventually be easy"

For presenting proofs, I would only use terminology such as "obviously", "clearly", "routine", etc if it would be for a course just below the class had the student had 'perfect' recollection. For ...
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10 votes

Examples of Mathematical Slang

How about the shoelace formula for the area of an arbitrary simple polygon?                     (Image from Wikipedia.) The formula computes the ...
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10 votes
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What is it called when terms disappear when reducing fractions?

If you continue the operations until $$\require{cancel}\frac{x}{b}=\frac{c}{b},\qquad\left(\frac{x}{b}\right)b=\left(\frac{c}{b}\right)b,\qquad x\left(\frac{b}{b}\right)=c\left(\frac{b}{b}\right),\...
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9 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Educator here who has worked with many students in the aforementioned age range (9-13) on triangles and squares. In my experience, it has never come up that a confusion between the boundary and the ...
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8 votes

Examples of Mathematical Slang

If you simplify a term by adding and subtracting something you call this a "nahrhafte Null" in German (probably translates to "nutritious null"?).
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  • 2,932
8 votes

Examples of Mathematical Slang

I often refer to the identities $(AB)^{-1} = B^{-1}A^{-1}$ or $(AB)^T = B^TA^T$ as the socks-shoes identity. I'm not sure how wide-spread this is, I certainly did not invent it and I'm pretty sure I'...
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8 votes

Examples of Mathematical Slang

In Russian, the Squeeze Theorem (a.k.a. The Pinching Theorem) is called "Теорема о двух милиционерах" — "Two Policemen Theorem". The idea is that if two policemen are holding a criminal between ...
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8 votes

What is it called when terms disappear when reducing fractions?

In general, as others have noted, if you have an equation such as $$\frac{x}{b}=\frac{c}b$$ The step to get from there to $$x=c$$ is typically referred to as cancelling the denominator. More generally,...
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8 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

I confess, when you start talking about 1-D triangles, my own first thought is "how can you have non-colinear points in 1-D?". So, I imagine most students that age will have a far more ...
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  • 81
7 votes
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Language as a barrier to learn math

Some examples: "One plus five squared" could be read as $(1+5)^2$ or $1+5^2$. This is a well-known ambiguity in natural language, for example in the following sentence I saw a man on a hill with a ...
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  • 8,729
7 votes
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Phrasing the Van Hiele levels in student-friendly language

The argument has been made that this is sort of a misappropriation of the terms, because the levels are meant to define levels of understanding rather than levels of detail. I'm assuming what you're ...
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7 votes

Can we save the word "unique"?

To my mind the defintion "Every x has a unique f(x)" of one-to-one is problematic because "has a unique" is neither clear English nor precise. The definition is usually stated as "$f(x) = f(y)$ ...
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  • 5,083
7 votes

How to word this exercise about converting "English" into interval notation?

This is my suggestion. Write each set of numbers in interval notation. (a) All real numbers between 5 and 7, including 5 but not including 7. (b) All real numbers between 1 and 10, including both 1 ...
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  • 6,795
7 votes

What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

Many of the geometric figures are so elementary that they are deeply rooted in daily language, and there seems to be no great solution. I agree with you here, and I think this is the key point. To me ...
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6 votes

Examples of Mathematical Slang

My elementary students always wanted to know the name of the symbol shown here: We called it the division house as did many of my colleagues, but my students wanted a mathematical name. We therefore ...
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  • 6,795
6 votes

Can students tell the difference between the "definition if" and the "theorem if"?

iff and if In my experience, students who have a solid grasp of first-order logic have absolutely no problem with the inconsistent use of "if" in definitions. The problem is that most ...
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  • 2,261
6 votes

Distinction between problems (such as equations), and universal truths

I am comfortable saying "Solve the equation $x+2$=4" and also saying "Using the equation $(a+b)(a-b)=a^2-b^2$, we see that...". On other other hand I would only ever speak of solving an equation, not ...
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